Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in strong-field-ionized liquid water

A unified picture of the electronic relaxation dynamics of ionized liquid water has remained elusive despite decades of study. Here, we employ sub-two-cycle visible to short-wave infrared pump-probe spectroscopy and ab initio nonadiabatic molecular dynamics simulations to reveal that the excess electron injected into the conduction band (CB) of ionized liquid water undergoes sequential relaxation to the hydrated electron s ground state via an intermediate state, identified as the elusive p excited state. The measured CB and p-electron lifetimes are 0.26 ± 0.02 ps and 62 ± 10 fs, respectively. Ab initio quantum dynamics yield similar lifetimes and furthermore reveal vibrational modes that participate in the different stages of electronic relaxation, with initial relaxation within the dense CB manifold coupled to hindered translational motions whereas subsequent p-to-s relaxation facilitated by librational and even intramolecular bending modes of water. Finally, energetic considerations suggest that a hitherto unobserved trap state resides ~0.3-eV below the CB edge of liquid water. Our results provide a detailed atomistic picture of the electronic relaxation dynamics of ionized liquid water with unprecedented time resolution.

I'm sorry to say that I'm not excited about that paper. It deals with an old problem, i.e. the relaxation of the aqueous electron after photo-ionization of water. The experimental observation of a transient species in the NIR per se is not new, as the authors admit. It probably started with Ref 23 from 1997, where similar observations have been made. When I understand the authors correctly, what is supposed to be new is the interpretation of that transient species. They claim that it is a p-like wavefunction, rather than a continuously solvating s-like state. I however don't see how their new results would support that conclusion, i.e. in what sense a continuously moving absorption band contradicts their observation, while a discrete intermediate is in agreement. Independent of that, I'm pretty sure that p-like wavefunctions have been put forward before to explain this observation.
To further support their conclusion, the present "NAMD simulations". First, the level of theory is in essence not described in the main paper, but that would be very crucial as it has been shown in the past that the properties of the solvated electron very strongly depend on the level of description. Second, I don't understand how the assignment is done. The authors refer to Fig.3b, which shows a red and a blue lobe, which are called charge density in the figure caption. The two lobes of a porbital have opposite sign, but that is NOT charge density. I must misunderstand something completely.
In conclusion, the paper needs quite some attention to work out better the arguments. Independent of that, after 25 years of work on this question, I would no longer consider it the most exciting science.
Reviewer #2 (Remarks to the Author): The manuscript entitled "Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in ionized liquid water" by Low et al. (performed at the laboratory of prof. Loh and accompanied by theory calculations by Oleg Prezhdo) focuses on the electron formation upon multiphoton ionization or maybe excitation of liquid water. Even sixty years after its observation during pulse radiolysis, the hydrated electron remains to be somewhat enigmatic. For example, in 2010, the group of Benjamin Schwartz provocatively suggested a radically different view of the hydrated electron structure. The Science paper brought a huge excitement, with many research groups demonstrating that the outcome was just an artifact of poor electronic structure description. I make this lengthy historical introduction to emphasize that the general attractiveness of the subject should not compromise the attempt to understand in detail all the aspects of the theory and experiment. Below, I summarize some aspects I did not understand -and I might be easily wrong. Yet I would be happy to read the author's reaction.
My first question is whether the authors are sure what states are formed initially during the radiolysis. The strong field used in the work can electronically excite the molecule as well as ionize it. The excitation seems to lead to the observation of the very same hydrated electron. The authors should discuss in detail this aspect.
Relatively recently, the same process was investigated by time-resolved photoelectron spectroscopy in the laboratory of Hans-Jakob Wörner at ETH (see https://www.science.org/doi/10.1126/sciadv.aaz0385). TRPES is generally assumed to provide the most direct insight into the electronic structure, with both the energetics and anisotropy revealing the details of the dynamics. The initially formed electronic states seem to be much better selected in this case, demonstrating that both the excitation and ionization lead to the same product on a similar time scale. The interpretation is, naturally, different for both processes. The authors do not seem even aware of this work yet it seems to be an important anchor to their new study on a multiphoton generation of excess electrons. The work might be not fully relevant as it is done on clusters that are arguably solid-like. But is the difference large enough to ignore the comparison?
It would be fair to place the strong field generation of the hydrated electron in the title -it is one of the aspects marking a distinction from previous papers.
The experiments are accompanied by ab initio MD calculations. I found this part confusing. The theory is not described in the main text, the approach is not justified. The way how the timeresolved vibrational spectra were obtained needs for sure a deeper discussion. I think that Nature Communications is not particularly restrictive on the size of the manuscript and all details needed to reconstruct the simulations should be provided.
Some minor issues. The authors cite Sanche's hypothesis on the role of pre-solvated electrons in DNA damage. It should be fair to mention that the community remains unconvinced (and I like the hypothesis). To conclude, I find the study interesting yet more work should be invested into placing the present finding in a context. The study could be also more "honest" in the sense that alternative hypotheses to explain the data are used.
Reviewer #3 (Remarks to the Author): This is certainly a nice work providing some new insight into the ultrafast relaxation dynamics of the excess electron in ionized liquid water. Specifically, the authors suggest that the entire population of electrons injected into the water conduction band goes through a previously (unconfirmed) trap state in the band gap to subsequently form the equilibrated hydrated electron. I consider the new spectroscopic data, largely due to improved temporal resolution, and the accompanying theoretical computations, an important contribution in advancing our understanding of the respective ultrafast electronic relaxation processes, including their mechanistic details.
However, the results need to be discussed in much greater depth which includes to thoroughly relate to a number of findings from previous works, not addressed in the present manuscript. With the extended discussion the manuscript won't fit format the communication format, also considering the many necessary assumptions (I come back to that) the authors need to make in order to reach at their interpretation of the results. As much as I appreciate the authors' overall work, there is room for alternative conclusions. Furthermore, I am quite disappointed how little the authors comment on water being a large-band-gap semiconductor and the implications in the present context. There are also several experimental aspects that need to be addressed more thoroughly. In the following I provide some specific comments.
Pages 3,4: Regarding the multi-(1.96 eV) photon ionization, I wonder how well the order of the process can be controlled. My concern is that 'ionization' is not limited to the injection of electrons deep into the CB but also produces true photoelectrons, emitted into vacuum. This additional channel would presumably affect the interpretation of the data, and should be commented on. A related issue is if strong-field ionization can be considered to be equivalent to single-photon ionization with regard to the relaxation dynamics of the excess electron. To my understanding this is not obvious at all, and there may be a possibility that this has a signature in the experimental data.
Page 5: The authors say: "Moreover, the absorption maxima at ~1.3 mu and ~0.85 mu, extracted previously from global fitting of absorption spectra, are not observed in the present work." Is that a correct statement? There seems to be intensity near 1.3 mu, and the 0.85 mu range is not covered in Figure 2. The authors should explain the reason for this discrepancy (if real).
On the same page it also says: "…the use of ~8 -9 eV for photoionization, below the ~10-eV energy for vertically injecting eCB into liquid water26,27 ..." This is the point where I wished the authors attempted to consider liquid water as a semiconductor, and quantitatively relate to the size of water's band gap. This should be inspired by works of the Sprik (C. Adriaanse et al., JPCL 3, 3411, 2012) and Galli (A. Gaiduk et al., Nat Comm 9, 247, 2018) groups. Furthermore, as I had pointed out above, 10 eV photon energy corresponds also to the onset of producing true photoelectrons. How are these processes related, and how do they potentially affect each other? Wouldn't it be useful to explicitly address and distinguish these two channels? In fact, even the title of this manuscript can be misunderstood.
Page 7: It says: "The observed int ~ p and their similar isotope dependence strongly suggest that eint corresponds to ep, i.e., ep exists as an intermediate state in the electronic relaxation of ionized liquid water." I find this a very important result which should be discussed in greater detail though, expanding on the role of H2O+, and certainly that text should not be moved to the SI but rather be part of the Discussion section. Furthermore, I believe that the concept of a double-cavity structure is new, and the authors should emphasis this aspect further.
1 Reviewer #1 (Remarks to the Author): We are grateful to the reviewer for the thoughtful comments, which have enabled us to improve the manuscript. In the following, we provide a point-by-point response.
I'm sorry to say that I'm not excited about that paper. It deals with an old problem, i.e. the relaxation of the aqueous electron after photo-ionization of water. The experimental observation of a transient species in the NIR per se is not new, as the authors admit. It probably started with Ref 23 from 1997, where similar observations have been made. When I understand the authors correctly, what is supposed to be new is the interpretation of that transient species. They claim that it is a p-like wavefunction, rather than a continuously solvating s-like state. I however don't see how their new results would support that conclusion, i.e. in what sense a continuously moving absorption band contradicts their observation, while a discrete intermediate is in agreement. Independent of that, I'm pretty sure that p-like wavefunctions have been put forward before to explain this observation.
The electronic relaxation dynamics of ionized liquid water is indeed an "old problem", as the reviewer rightly points out. However, there are several limitations associated with the previous studies. First, the ~0.3-ps laser pulses that were employed in the early studies offer lower time resolution, resulting in the large uncertainties in the formation (110 -300 fs) and decay (240 -545 fs) times of the intermediate state that was invoked to explain the observed dynamics (see p. 5 of the original manuscript). Second, the use of relatively long laser pulses for driving ionization allow the hydrated electron that is produced by the leading edge of the laser pulse to be photoexcited by the trailing edge of the laser pulse, as pointed out in ref. 1 , thus further complicating analysis. Third, the use of few-millimeter-thick sample targets housed within cuvettes in previous measurements inevitably give rise to cross-phase modulation artifacts that can be misinterpreted as the ultrafast response of the sample, as shown in ref. 2 . Moreover, the group velocity mismatch between the pump and probe pulses further degrades the time resolution. Fourth, some of the most recent measurements, performed with improved ~0.1-ps time resolution, albeit with a narrower probe spectral range In this study, we bring to bear on this "old problem" sub-two-cycle laser pulses spanning the visible to near-infrared (0.5 -0.9 m) and the short-wave infrared (SWIR, 1.1 -1.7 m), made possible by recent advances in femtosecond laser technology. Our experimental data, along with the results obtained from theoretical simulations, enables us to reconstruct the most comprehensive picture of the ultrafast electronic relaxation dynamics of ionized liquid water to date. Our experimental results unambiguously resolve the sub-100-fs formation and subsequent decay of a pronounced SWIR absorption band. To further convince the reviewer that our experimental results support the existence of an intermediate state and that our ~10-fs time resolution greatly facilitates its observation, we first show the time-resolved differential absorption spectra in two limits, with ( While numerous studies found no need to invoke the existence of the intermediate, those that did variously referred to it as the "prehydrated electron" (ref. 5 ), the "wet electron" (refs. 2,6-8 and ), or the "weakly bound electron" (ref. 9 ). While the p state has indeed been put forth as the transient intermediate, e.g., see refs. 6 and 2 , we note that these assignments were made in the absence of supporting experimental evidence. On the other hand, our study resolves the lifetime of the transient intermediate as well as the isotope dependence of the lifetime, both of which are consistent with the characteristics of the p state deduced by the ultrafast To further support their conclusion, the present "NAMD simulations". First, the level of theory is in essence not described in the main paper, but that would be very crucial as it has been shown in the past that the properties of the solvated electron very strongly depend on the level of description. Second, I don't understand how the assignment is done. The authors refer to Fig.3b, which shows a red and a blue lobe, which are called charge density in the figure caption. The two lobes of a p-orbital have opposite sign, but that is NOT charge density. I must misunderstand something completely.
We thank the reviewer for this comment. Indeed, it is important to specify accurately the level of theory. We combine NAMD with ab initio real-time TDDFT, and we use the PBE0 functional with the fraction of the Hartree-Fock exchange increased to 40%, as established in the prior theoretical studies. We stated this and provided relevant references in the Supporting Information of the original manuscript. We did not adjust any parameters during our simulations, beyond what has been done in the published work. During the revision, we specified these computational details in the Methods section of the main text. (REV 1.5) Fig. 3b shows the wave function (orbital), not charge density. We thank the reviewer for catching this error. We have changed the caption accordingly. (REV 1.6) In conclusion, the paper needs quite some attention to work out better the arguments. Independent of that, after 25 years of work on this question, I would no longer consider it the most exciting science.
While it is true that the electronic relaxation dynamics of ionized liquid water has been investigated over a couple of decades, we believe that our unprecedented experimental time resolution allows us to reconstruct the most comprehensive picture for the electronic relaxation dynamics of ionized liquid water to date, thus shedding new insight into this "old problem". Further, the reported ab initio NAMD simulations are the first of a kind.

Fig. R2.
Comparison of the simulated time-resolved differential absorption spectra when the conduction-band electron relaxes via the p state to the s state, as observed with a Gaussian FWHM instrument response function of (a) 10 fs and (b) 300 fs. The color scale is the differential absorption signal in arbitrary units. Note that both plots employ the same color scale. It is evident that the observation of the SWIR absorption at early time delays is hampered when the time resolution is ~300 fs, even in the absence of coherent artifacts.
Previously, NAMD simulations of solvated electrons have been performed at a much simpler, pseudopotential level of electronic structure theory. Conversely, ab initio studies of solvated electrons did not model NA excited state dynamics. The current simulation is first to perform NAMD of the hydrated electron at the ab initio (DFT) level of electronic structure theory. To stress the theoretical novelty, we emphasize this fact on p. 7 of the revised manuscript. (REV 1.7) 5 Reviewer #2 (Remarks to the Author): The manuscript entitled "Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in ionized liquid water" by Low et al. (performed at the laboratory of prof. Loh and accompanied by theory calculations by Oleg Prezhdo) focuses on the electron formation upon multiphoton ionization or maybe excitation of liquid water. Even sixty years after its observation during pulse radiolysis, the hydrated electron remains to be somewhat enigmatic. For example, in 2010, the group of Benjamin Schwartz provocatively suggested a radically different view of the hydrated electron structure. The Science paper brought a huge excitement, with many research groups demonstrating that the outcome was just an artifact of poor electronic structure description. I make this lengthy historical introduction to emphasize that the general attractiveness of the subject should not compromise the attempt to understand in detail all the aspects of the theory and experiment. Below, I summarize some aspects I did not understand -and I might be easily wrong. Yet I would be happy to read the author's reaction.
We are grateful to the reviewer for the thoughtful comments for giving us the opportunity to respond to them. We believe that the manuscript has been improved following our addressing of the comments. In the following, we provide a point-by-point response.
My first question is whether the authors are sure what states are formed initially during the radiolysis. The strong field used in the work can electronically excite the molecule as well as ionize it. The excitation seems to lead to the observation of the very same hydrated electron. The authors should discuss in detail this aspect.
We thank the reviewer for this comment. In this work, we employ intense, few-cycle laser pulses to strong-field ionize liquid water. Due to the use of these intense, few-cycle pulses and the occurrence of strong-field ionization on the sub-cycle timescale, we believe that the electron is injected vertically into the conduction band (CB). An earlier study that probed the THz response of the CB electron, prepared by the strong-field ionization of liquid water, arrived at the same conclusion (ref. 15 ). As such, it is conceivable that strong-field ionization leads to the same hydrated electron species that would be produced by radiolysis. In other words, the electronic relaxation processes that are observed in this work are also applicable to those induced by conventional radiolysis. We have clarified this on p. 4 of the revised manuscript. (REV 2.1) Relatively recently, the same process was investigated by time-resolved photoelectron spectroscopy in the laboratory of Hans-Jakob Wörner at ETH (see https://www.science.org/doi/10.1126/sciadv.aaz0385). TRPES is generally assumed to provide the most direct insight into the electronic structure, with both the energetics and anisotropy revealing the details of the dynamics. The initially formed electronic states seem to be much better selected in this case, demonstrating that both the excitation and ionization lead to the same product on a similar time scale. The interpretation is, naturally, different for both processes. The authors do not seem even aware of this work yet it seems to be an important anchor to their new study on a multiphoton generation of excess electrons. The work might be not fully relevant as it is done on clusters that are arguably solid-like. But is the difference large enough to ignore the comparison?
We thank the reviewer for this comment. We are aware of the said work by the Wörner group 16 . That work reported the observation of ultrafast proton/hydrogen atom transfer dynamics and electron hydration dynamics following either 15.5-eV ionization or 9.3-eV excitation of water clusters, (H2O)Nꞏ + ( ~ 400). As the reviewer had guessed, we did not reference this work in our original manuscript because our results are not directly comparable to those obtained from water clusters due to their finite size, as we will explain below, as well as the possible ice-like nature of these large water clusters (it has been shown that water clusters with ≳ 275 exhibit ice-like behavior [DOI: 10.1126/science.1225468]). We now see the omission of the work by the Wörner group as a shortcoming that we would like to address in the revised manuscript. This work is cited as ref. 33 in the revised manuscript.
The investigation by the Wörner group did not find any evidence for the existence of a transient intermediate state. The measured photoelectron asymmetry parameter, found to be independent of pump-probe time delay, is suggestive of a hydrated electron with an isotropic angular distribution. From there, it was inferred that the electron produced by ionization relaxes directly to the electronic ground state of the hydrated electron, albeit in a vibrationally excited state, without passing through the intermediate p state. We consider a few factors that could explain the discrepancy between their result and ours. First, unlike the non-vanishing anisotropy parameter that was previously observed for the photoexcited hydrated electron, in which orbital alignment was imprinted by photoexcitation of the hydrated electron with linearly polarized light (ref. 13 ), any p state that is produced in Wörner's experiment would have originated from relaxation of the conduction-band electron, during which orbital dealignment could occur. Loss of orbital alignment then yields the observed isotropic angular distribution. Second, our use of strong-field ionization favors the injection of an electron vertically into the CB. This is in contrast with Wörner's group use of 9.3-eV (133-nm) photoexcitation, which lies below the energy threshold required to inject an electron vertically into the CB. In that case, the observed ultrafast dynamics is explained in terms of H2O undergoing sub-50-fs photodissociation to yield the hydronium radical (H3Oꞏ), which then autoionizes to yield H3O + and the s* electron, thus circumventing the p state entirely. Third, in the experiments by the Wörner group that employ 15.5-eV (80-nm) vertical ionization, we note that the expected ejection length of 〈 〉 ~ 3.8 nm 17 exceeds the ~1.4-nm radius of the water cluster. As such, it is conceivable that the hydrated electron and its precursor, if any, are initially localized on the surface of the cluster. The abundance of surface defects and the low solvent reorganization energy requirements further favor the formation of a hydrated electron at the surface 18 . Considering that a surface-bound, groundstate hydrated electron has a low binding energy of ~1.6 eV 18 or less 19 , and that its internalization and hence, concomitant increase in binding energy, occurs on a timescale of ~0.5 ps 19 , the p excited state of the hydrated electron might not even exist as a bound state on the surface if we assume that the s -p energy gap on the surface is unchanged from the bulk value of 1.7 eV. Under such circumstances, one would expect the p state to be energetically inaccessible during the electronic relaxation of ionized water clusters, i.e., the conductionband electron relaxes directly to the s* state. Fourth, we note that their experimental time resolution of ~85 fs FWHM is lower than the ~10-fs time resolution available in the present study; as such, it is conceivable that the short-lived p state, even if it had been formed, might have eluded detection. We have added this comparison, which we believe provide a context for our work, to p. 13 -14 of the revised manuscript.

(REV 2.2)
It would be fair to place the strong field generation of the hydrated electron in the title -it is one of the aspects marking a distinction from previous papers.
We thank the reviewer for this suggestion. We have revised the title to "Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in strongfield-ionized liquid water". (REV 2.

3)
The experiments are accompanied by ab initio MD calculations. I found this part confusing. The theory is not described in the main text, the approach is not justified. The way how the time-resolved vibrational spectra were obtained needs for sure a deeper discussion. I think that Nature Communications is not particularly restrictive on the size of the manuscript and all details needed to reconstruct the simulations should be provided.
We thank the reviewer for asking us to provide simulation details in the main text. Indeed, the original version of the paper gave such details in the Supporting Information. During the revision, we included the key simulation details in the main text. The quantum dynamics simulation methodology combined NAMD for the description of quantum transitions within the electronic manifold and interactions between electrons and nuclei, with real-time TDDFT for evolution of the electronic subsystem. Such methodology has been used successfully with a broad range of condensed phase and molecular systems. We did use a larger-than-normal fraction of the Hartree-Fock exchange in the PBE0 DFT functional. This is needed for proper description of the hydrated electron properties, as established in prior theoretical works. We state this and cited these works in the Methods section, now added to the Methods section of the main text in the revised manuscript.

(REV 2.4)
To obtain the time-resolved vibrational spectra, more specifically, the electron-phonon influence spectra, we computed Fourier transforms of the energy gaps between the initial and final states, i.e., between the lowest energy conduction band state and p state, and between the p and s states. To obtain time-resolution, the Fourier transforms are computed for the parts of the trajectories in which the electron is already relaxed to the initial state for each transition. Because these trajectory parts are relatively short, the spectral resolution is relatively low. Nevertheless, the influence spectra can clearly identify what kind of modestranslational, librational, internal bending -are participating in a particular transition because the frequencies of these motions differ by hundreds of cm -1 . We have added these details to the Methods section of the main text during the revision. (REV 2.5) Some minor issues. The authors cite Sanche's hypothesis on the role of pre-solvated electrons in DNA damage. It should be fair to mention that the community remains unconvinced (and I like the hypothesis).
We thank the reviewer for pointing this out. We have revised the last sentence of the first paragraph to read, "The electrons, on the other hand, are known postulated to induced genomic damage by dissociative electron attachment 5 ." (REV 2.6) Figure 4 should be augmented, adding especially all recent photoemission data.
We thank the reviewer for this suggestion. We have added to the text that accompanies Fig. 4 a range of energetic parameters obtained from recent studies; please see p. 17 of the revised manuscript. (REV 2.7) To conclude, I find the study interesting yet more work should be invested into placing the present finding in a context. The study could be also more "honest" in the sense that alternative hypotheses to explain the data are used. 8 We thank the reviewer for finding our work interesting. We believe that our discussion of the limitations encountered in earlier optical pump-probe measurements of ionized liquid water (REV 1.1) and the comparison to the recent work by the Wörner group on ionized water clusters (REV 2.2) provide more context for our findings. Beyond these, we have also inserted into p. 13 -15 of the revised manuscript a brief discussion of the recent studies by the Signorell 20,21 and Suzuki 22 groups, performed on water clusters, (H2O)Nꞏ + (〈 〉 ~ 300), and liquid water, respectively. Neither study observed the p state intermediate, perhaps due to the limited ~70 -220 fs time resolution of the experimental setups and coherent artifacts obfuscating the early-time dynamics. In addition, similar to the situation encountered in the study by the Wörner group, the cluster study by the Signorell group is complicated by the ejection length 〈 〉 ~ 3.2 nm being greater than the dimension of the water cluster, thus favoring initial localization of the electron on the surface, where the p state might be energetically inaccessible. (REV 2.8) We thank the reviewer for encouraging us to explore possible alternative hypotheses to explain our data. In the revised manuscript, we now consider three additional possibilities.  Fig. R1a). Second, beyond the p state, we also consider the involvement of the hypervalent hydronium radical species, H3Oꞏ, as an intermediate state. In previous time-resolved photoelectron spectroscopy studies, the formation of s* electrons following 9.3-eV photoexcitation of water clusters 16 and 7.7-eV photoexcitation of liquid water 22 to the electronically excited state was attributed to the dissociation of H2O to yield the H3Oꞏ radical, which then autoionizes to yield H3O + and the s* electron, i.e., H2O* (aq) + H2O (l) → H3Oꞏ (aq) + OHꞏ (aq)  17 , which then undergoes the sequential relaxation process outlined in the manuscript. Our experiments are unable to distinguish the formation of the CB electron via the autoionization or vertical ionization channels because they do not probe the spectroscopic observable of CB electrons, located in the terahertz. Future experiments that probe the terahertz absorption of ionized liquid water can resolve the delayed appearance of CB electrons that is associated with the autoionization channel. We have added the above discussion to p. 12 -13 of the revised manuscript. (REV 2.9)

Reviewer #3 (Remarks to the Author):
This is certainly a nice work providing some new insight into the ultrafast relaxation dynamics of the excess electron in ionized liquid water. Specifically, the authors suggest that the entire population of electrons injected into the water conduction band goes through a previously (unconfirmed) trap state in the band gap to subsequently form the equilibrated hydrated electron. I consider the new spectroscopic data, largely due to improved temporal resolution, and the accompanying theoretical computations, an important contribution in advancing our understanding of the respective ultrafast electronic relaxation processes, including their mechanistic details.
We thank the reviewer for considering our work an important contribution to advancing the understanding of the ultrafast electronic relaxation processes in ionized liquid water. At the same time, we are also grateful to the reviewer for the thoughtful comments, which have allowed us to improve the manuscript. In the following, we provide a point-by-point response.
However, the results need to be discussed in much greater depth which includes to thoroughly relate to a number of findings from previous works, not addressed in the present manuscript. With the extended discussion the manuscript won't fit format the communication format, also considering the many necessary assumptions (I come back to that) the authors need to make in order to reach at their interpretation of the results. As much as I appreciate the authors' overall work, there is room for alternative conclusions. Furthermore, I am quite disappointed how little the authors comment on water being a large-band-gap semiconductor and the implications in the present context. There are also several experimental aspects that need to be addressed more thoroughly. In the following I provide some specific comments.
The reviewer's comments about relating our results to previous findings and offering alternative interpretations of the results are well-taken. During the revision of the manuscript, we discuss critically the limitations encountered in the earlier studies, which prevented a consensus for the existence of the intermediate state from being established, and furthermore we put our work in a broader context by discussing our findings in relation to recent results obtained from the time-resolved photoelectron spectroscopy of ionized water clusters and liquid water. More details are given below.
Earlier studies of the electronic relaxation dynamics of ionized liquid water encountered several limitations. First, the ~0.3-ps laser pulses that were employed in the early studies offer lower time resolution, resulting in the large uncertainties in the formation (110 -300 fs) and decay (240 -545 fs) times of the intermediate state that was invoked to explain the observed dynamics (see p. 5 of the original manuscript). Second, the use of relatively long laser pulses for driving ionization allow the hydrated electron that is produced by the leading edge of the laser pulse to be photoexcited by the trailing edge of the laser pulse, as pointed out in ref. 1 , thus further complicating analysis. Third, the use of few-millimeter-thick sample targets housed within cuvettes in previous measurements inevitably give rise to cross-phase modulation artifacts that can be misinterpreted as the ultrafast response of the sample, as shown in ref. 2  On p. 13 -15 of the revised manuscript, we compare our results to the recent report by the Wörner group on the ultrafast dynamics induced by the ionization of water, albeit in the form of clusters, (H2O)Nꞏ + ( ~ 400) 16 . Their investigation did not find any evidence for the existence of a transient intermediate state. The measured photoelectron asymmetry parameter, found to be independent of pump-probe time delay, is suggestive of a hydrated electron with an isotropic angular distribution. From there, it was inferred that the electron produced by ionization relaxes directly to the electronic ground state of the hydrated electron, albeit in a vibrationally excited state, without passing through the intermediate p state. We consider a few factors that could explain the discrepancy between their result and ours. First, unlike the non-vanishing anisotropy parameter that was previously observed for the photoexcited hydrated electron, in which orbital alignment was imprinted by photoexcitation of the hydrated electron with linearly polarized light (ref. 13 ), any p state that is produced in Wörner's experiment would have originated from relaxation of the conduction-band electron, during which orbital dealignment could occur. Loss of orbital alignment then yields the observed isotropic angular distribution. Second, our use of strong-field ionization leads to the injection of an electron vertically into the CB. This is in contrast with Wörner's group use of 9.3-eV (133-nm) photoexcitation, which lies below the energy threshold required to inject an electron vertically into the CB. In that case, the observed ultrafast dynamics is explained in terms of H2O undergoing sub-50-fs photodissociation to yield the hydronium radical (H3Oꞏ), which then autoionizes to yield H3O + and the s* electron, thus circumventing the p state entirely. Third, in the experiments by the Wörner group that employ 15.5-eV (80-nm) vertical ionization, we note that the expected ejection length of 〈 〉 ~ 3.8 nm 17 exceeds the ~1.4-nm radius of the water cluster. As such, it is conceivable that the hydrated electron and its precursor, if any, are initially localized on the surface of the cluster. The abundance of surface defects and the low solvent reorganization energy requirements further favor the formation of a hydrated electron at the surface 18 . Considering that a surface-bound, groundstate hydrated electron has a low binding energy of ~1.6 eV 18 or less 19 , and that its internalization and hence, concomitant increase in binding energy, occurs on a timescale of ~0.5 ps 19 , the p excited state of the hydrated electron might not even exist as a bound state on the surface if we assume that the s -p energy gap on the surface is unchanged from the bulk value of 1.7 eV. Under such circumstances, one would expect the p state to be energetically inaccessible during the electronic relaxation of ionized water clusters, i.e., the conductionband electron relaxes directly to the s* state. Fourth, we note that their experimental time resolution of ~85 fs FWHM is lower than the ~10-fs time resolution available in the present study; as such, it is conceivable that the short-lived p state, even if it had been formed, might have eluded detection. Here, we also note the recent studies by the Signorell 20,21 and Suzuki 22 groups, performed on water clusters, (H2O)Nꞏ + (〈 〉 ~ 300), and liquid water, respectively. Neither study observed the p state intermediate, perhaps due to the limited ~70 -220 fs time resolution of the experimental setups and coherent artifacts obfuscating the early-time dynamics. In addition, similar to the situation encountered in the study by the Wörner group, the cluster study by the Signorell group is complicated by the ejection length 〈 〉 ~ 3.  17 , which then undergoes the sequential relaxation process outlined in the manuscript. Our experiments are unable to distinguish the formation of the CB electron via the autoionization or vertical ionization channels because they do not probe the spectroscopic observable of CB electrons, located in the terahertz. Future experiments that probe the terahertz absorption of ionized liquid water can resolve the delayed appearance of CB electrons that is associated with the autoionization channel. (REV 3.

3)
Please see below for our response to the point that the reviewer had raised about water being a large band-gap semiconductor.
Pages 3,4: Regarding the multi-(1.96 eV) photon ionization, I wonder how well the order of the process can be controlled. My concern is that 'ionization' is not limited to the injection of electrons deep into the CB but also produces true photoelectrons, emitted into vacuum. This additional channel would presumably affect the interpretation of the data, and should be commented on. A related issue is if strong-field ionization can be considered to be equivalent to single-photon ionization with regard to the relaxation dynamics of the excess electron. To my understanding this is not obvious at all, and there may be a possibility that this has a 13 signature in the experimental data.
We thank the reviewer for this comment. Our pump fluence dependence measurements (see Section 3 of the Supplementary Information) give photon orders that are very close to four (4.07 ± 0.07 with visible probing and 3.99 ± 0.01 with SWIR probing). This result indicates that a four-photon resonance enhanced multiphoton ionization process dominates strong-field ionization. As the reviewer points out, strong-field ionization also leads to the ejection of electrons from the bulk liquid. However, these photoelectrons, detected in photoemission experiments, do not form hydrated electrons and therefore do not contribute to our transient absorption signal, which probe the electron dynamics within the bulk liquid. We have clarified this on p. 4 -5 of the revised manuscript. (REV 3.4) The reviewer also asks if strong-field ionization and single-photon ionization can be considered to be equivalent. In this work, we employ intense, few-cycle laser pulses to strong-field ionize liquid water. Due to the use of these intense, few-cycle pulses and the occurrence of strong-field ionization on the sub-cycle timescale, we believe that the electron is injected vertically into the CB. (An earlier study that probed the THz response of the CB electron, prepared by the strong-field ionization of liquid water, arrived at the same conclusion 15 .) As such, we believe that strong-field ionization and single-photon ionization are equivalent in the sense that both involve vertical transitions. This has already been clarified on p. 3 -4 of the original manuscript.
Page 5: The authors say: "Moreover, the absorption maxima at ~1.3 mu and ~0.85 mu, extracted previously from global fitting of absorption spectra, are not observed in the present work." Is that a correct statement? There seems to be intensity near 1.3 mu, and the 0.85 mu range is not covered in Figure 2. The authors should explain the reason for this discrepancy (if real).
We thank the reviewer for this comment. We would like to point out that the sentence in the manuscript pertains to the location of the absorption maxima. While our data shows that the SWIR absorption is broad, with significant transient absorption at 1.3 m, the absorption maximum clearly resides at longer wavelengths (~1.6 m). We would also like to point out that 0.85 m is covered in Fig. 2a (the horizontal axis spans 600 -900 nm).
On the same page it also says: "…the use of ~8 -9 eV for photoionization, below the ~10-eV energy for vertically injecting eCB into liquid water26,27 ..." This is the point where I wished the authors attempted to consider liquid water as a semiconductor, and quantitatively relate to the size of water's band gap. This should be inspired by works of the Sprik (C. Adriaanse et al., JPCL 3, 3411, 2012) and Galli (A. Gaiduk et al., Nat Comm 9, 247, 2018) groups. Furthermore, as I had pointed out above, 10 eV photon energy corresponds also to the onset of producing true photoelectrons. How are these processes related, and how do they potentially affect each other? Wouldn't it be useful to explicitly address and distinguish these two channels? In fact, even the title of this manuscript can be misunderstood.
We thank the reviewer for this comment and for referring us to the works by Sprik and Galli, now cited in the revised manuscript as refs. 42 and 43, respectively. The reviewer seeks to make a connection between our measurement results and the large band gap of liquid water.
With liquid water at its equilibrium geometry, the (vertical) band gap is ~10 -11 eV; these values are obtained by considering the recently reported vertical ionization potential (11.33 eV) 26,27 and the various computed vertical electron affinities (0.2, 0.74, 0.97, 1.1 eV) 28-31 of liquid water. Allowing for solvent reorganization leads to a reduced (adiabatic) band gap of ~7 eV 32,33 . While our experiments do not measure these energetic parameters -our experiments probe the relaxation from the CB to the various hydrated electron states (in the terminology of semiconductor physics, these states would correspond to defect levels in the band gap) -they nevertheless determine the accessible ionization mechanisms. When the total energy deposited by the pump pulse exceeds the vertical band gap, the electron is injected vertically into the CB. When the total energy deposited by the pump pulse falls between the vertical and adiabatic band gaps, however, the CB electron is produced via autoionization, which involves solvent reorganization and therefore a possible change in the electronic relaxation timescales. On p. 13 of the revised manuscript, we explain these ionization mechanisms in relation to the vertical and adiabatic band gaps of liquid water.

(REV 3.5)
The ejection of photoelectrons does not affect the experimental results, as we had explained above in relation to an earlier comment from this reviewer (please see REV 3.1), because our measurements probe the transient absorption of excess electrons in the bulk liquid, independent of photoelectrons that are ejected from the liquid jet. Moreover, our use of the term "ionization" is consistent with the literature, where the removal of an electron from a water molecule, regardless of whether the electron is injected into the CB or into vacuum (as a photoelectron), is referred to as "ionization"; please see, for example, refs. 1,4,5,34,35 . We also note that the appearance of "excess electron" in the title should clarify that the electron is injected into the CB. The advice by the reviewer to expand upon the discussion associated with our assignment of the intermediate state to the p electron is well-taken. Accordingly, we have added the following discussion to p. 15 -16 of the revised manuscript. First, we note that our experiments on ionized liquid water and other experiments on the excited-state dynamics of the hydrated electron involve different initial solvent configurations. In the case of ionized liquid water, the initial solvent configuration is that of liquid water at equilibrium. In the case of the excited-state dynamics of the hydrated electron, however, the hydrated electron initially resides in a solvent cavity of dimensions comparable to the radius of gyration of the hydrated electron (2.44 Å) 36 . Hence, our assignment of the intermediate state to the p state suggests that solvent reorganization within the timescale for relaxation from the CB (~0.3 ps) yields the solvent configuration of the hydrated electron. This is supported by the ab initio NAMD simulations that show relaxation of the high energy excited electron from deep inside in the CB to the p shaped state exhibiting two lobes (Fig. 3b). Second, unlike the experiments on the excited-state dynamics of the hydrated electron, where the observed ultrafast dynamics is associated solely with the hydrated electron, ionized liquid water simultaneously exhibits both electron and hole dynamics. Therefore, while our present study focuses on the electronic relaxation dynamics, it is important to realize that the valence hole created by ionization undergoes ultrafast temporal evolution at the same time 35,[37][38][39] . According to ab initio molecular dynamics simulations, the initially delocalized valence hole localizes on the ~30-fs timescale onto a single water molecule, forming the H2Oꞏ + radical cation 35,37 , which subsequently undergoes proton transfer to a neighboring water molecule to produce the hydronium ion, H3O + , and the hydroxyl radical, OHꞏ. A recent femtosecond soft X-ray absorption study found a timescale of ~50 fs for this ultrafast proton transfer reaction 37 . An obvious question that arises is the extent to which electronic relaxation dynamics is affected by hole localization and subsequent proton transfer. The latter is accompanied by the contraction of the intermolecular OꞏꞏꞏO distance between H2Oꞏ + and the neighboring H2O molecules in its immediate vicinity. The contraction of the OꞏꞏꞏO bond (to 2.4 Å) promotes proton transfer, whereupon the OꞏꞏꞏO distance returns to that of equilibrium neutral water (2.7 Å). It is conceivable that the valence hole-induced solvent reorganization dynamics could interfere with the electronic relaxation dynamics. However, we note that our ab initio nonadiabatic molecular dynamics simulations reproduce the timescales for the electronic relaxation dynamics even though they do not consider the competing hole dynamics. Moreover, an ejection length of ~40 Å, determined from a recent time-resolved THz study of strong-field-ionized liquid water 15 , implies that the initial ionization site and the site at which the electron localizes to form the p state is separated by a distance of ~16 solvent shells. The large electron-hole separation produced by strong-field ionization provides a plausible explanation for the absence of any interference between the electron and hole dynamics.

(REV 3.7)
The ab initio NAMD simulations demonstrate that the p state contains two lobes, as expected, and that the two lobes occupy two adjacent cavities. The earlier NAMD simulations based on a single-particle pseudopotential description of the hydrated electron showed that the p state occupied an elongated cavity that turned into a spherical cavity upon relaxation to the s state 40 . The current ab initio DFT level of theory, which includes not only the extra electron but also the valence electrons of all the water molecules, produces a somewhat different structure. The two lobes of the p state are separated by a low electron density region that allows a few water molecules to penetrate between the lobes. This double-cavity type structure occurs because the p state has a node in the middle, and in the absence of electron density at the node, there is no Pauli repulsion that pushes electrons of water molecules away from this region. The pseudopotential approach employed in earlier studies either creates an elongated single cavity 40 or no cavity 41 , depending on the pseudopotential parameters. The more sophisticated ab initio description that includes all the valence electrons allows the double-cavity to be formed, with water molecules pushed away from the regions of high p electron density and allowing water molecules to penetrate regions of low p electron density near the node. We have added this point to p. 11 of the revised manuscript. (REV 3.8) Pages 9,10: I am quite puzzled by the energy values that were chosen on page 9 (bottom), and then used to construct Figure 4. Specifically, why have the authors chosen VDE = 3.76 eV and not lower values? But the bigger worry is the Vo = 0.97 eV value. Admittedly, this value has been debated for a long time. Not mentioning that it is likely much smaller (Gaiduk et al.) is not helpful since there are alternatives to construct such energy diagram. This being said, it is very difficult to understand all the information contained in Figure 4 unless more description and guidance is provided.
We thank the reviewer for this comment. Amongst the parameters that are extracted from the literature and presented in Fig. 4 -the vertical electron affinity ( ), adiabatic electron affinity (AEA), vertical detachment energy (VDE), and transition energy of the hydrated electron ( ) -there is greatest degree of uncertainty surrounding VDE and . (Please also note that the estimation of the energetic position of e † does not require knowledge of AEA.) The VDE value that we have chosen is from a recent study in which extreme ultraviolet (EUV) probe pulses were employed 42 . Under these conditions, it is found that the measured photoelectron kinetic energy distributions are relatively insensitive to inelastic scattering within the liquid, thereby enabling the accurate retrieval of the VDE (3.76 ± 0.05 eV). We also note that the VDE obtained from EUV probing is comparable to that obtained from an earlier study that employed multi-wavelength UV probing with energy-dependent corrections for electron scattering (3.7 ± 0.1 eV) 21,43 . Without corrections for electron scattering, the measured VDEs are found to be generally lower, in the range of 3.2 -3.7 eV [44][45][46][47] .
As alluded to by the reviewer, a definitive value for has remained elusive to date. In our original manuscript, we chose to use the value 0.97 eV, obtained from thermodynamic integration using hybrid functionals without the inclusion of nuclear quantum effects 30 . We thank the reviewer for drawing our attention to the important work by Gaiduk et al. 28 , which combined path-integral molecular dynamics with non-self-consistent G0W0 calculations starting from hybrid functional wave functions to yield of 0.2 eV. In the revised manuscript, we consider these values as well as that from a follow-up work by Ziaei and Bredow (1.1 eV) 31 , performed at the self-consistent GW level of theory with implicit vertex corrections, albeit on a smaller simulation cell (32 vs. 64 water molecules used by Gaiduk). On p. 17 -18 of the revised manuscript, we now cite obtained from these various studies and note that its value has been a subject of debate. (REV 3.10) Furthermore, on p. 16 -17 of the revised manuscript, we now provide definitions of the various parameters that appear in Fig. 4. (REV 3.11)